Three-dimensional fractal model of normal contact damping of dry-friction rough surface

摘要

According to the influence of the normal contact damping of joint surfaces on the dynamic characteristics of high-precision machinery (machine tool, robot, etc.), in this article, a three-dimensional fractal model of normal contact damping of dry-friction rough joint surfaces based on Hertz theory and fractal theory is established. The three-dimensional surface topography is constructed, according to the modified double variable Weierstrass–Mandelbrot function. The fractal model of strain energy [Formula: see text], dissipated energy [Formula: see text], damping loss factor [Formula: see text], and normal contact damping [Formula: see text] are deduced in detail, and the influence of fractal parameters and dynamic friction coefficient [Formula: see text] on them are simulated. The simulation curves show that strain energy [Formula: see text], dissipated energy [Formula: see text], damping loss factor [Formula: see text], and normal damping [Formula: see text] increase with the increase in the fractal roughness G; the influence of fractal dimension D on [Formula: see text] is more changeable, first [Formula: see text] decreases with the increase in D and then increases. [Formula: see text], [Formula: see text], and [Formula: see text] increase with the increase in D and [Formula: see text], respectively; the effect of [Formula: see text] on [Formula: see text] is not obvious, so simple change in [Formula: see text] has no significant change in [Formula: see text]; a comparative analysis of the theoretical calculation of normal damping and experimental results show that their general trend is consistent, and they increase with the increase in total normal contact load P, the relative error is 5%–25%. The theoretical model can provide reference for the design of normal contact damping of the joint surfaces.